Project Summary In humans, genetic variation is distributed geographically, reflecting the history of human movements across the continents. Understanding these spatial patterns is crucial for many fields in human population genomics, including the study of human evolutionary history and linking genotypes and phenotypes. Historically, limi- tations in the size and scope of empirical datasets have allowed researchers to employ models that ignore geography, but modern genomic datasets demand population genetic methods that incorporate geographic space. The proposed research will generate novel statistical methods that incorporate geography into the study of population genetic structure, admixture, demography, and natural selection. These methods will be developed and implemented as open-source software, validated using state-of-the-art forward-time simula- tions, and applied to publicly available human genomic datasets. We will develop tests for population admixture that explicitly account for geographic patterns due to isolation by distance. These tests will be used to analyze densely sampled Eurasian human genomic datasets to identify admixed samples, and will also be applied in sliding windows along the genome to highlight genomic regions that may have been transferred between populations via adaptive introgression. We will also develop a spatiotemporal population clustering method that can jointly analyze ancient and modern samples. Neutral genetic processes are expected to generate population differentiation between samples separated in space or time, so this clustering method will account for both when determining whether two samples share ancestry in the same discrete population. This method will be extended to detect selection on polygenic traits by testing for an aggregate increase in the frequency of alleles involved in a particular trait relative to the neutral expectation. We will apply this method to test for selection through time on human height across Eurasia. Finally, we will model the lengths of shared genomic segments between individuals, which are informative about genealogical overlap at different points in the past, to learn about how population density and dispersal patterns have changed across geographic space through time. The proposed work represents advances in a number of fields in statistical population genetics, including the detection of population admixture, adaptive introgression, population replacement and the joint analysis of DNA from ancient and modern samples, detecting selection on polygenic traits, and modeling heterogeneity in demographic processes through time. Taken together, this work will offer empirical researchers a valuable toolkit for the analysis of modern genomic datasets, which require spatially explicit methods, and will shed light on both human evolutionary history and the mechanisms by which humans have adapted to their environment across space and time.